Answer to Question #3028 in Geometry for James

Question

I have a maths problem that I'm having difficulty solving for a literary work. I have an equilateral triangle with sides of 3 km. I already calculated the height to be 2.6 km roughly by Pythagoras's theorem and from there, I worked out the area to be 4 km/sq. I may have gotten these figures wrong so feel free to correct me. My problem is I'm trying to figure out how many rectangular sections of 50 meters by 25 meters I can divide the triangle into roughly. I understand that the shape means that not every section can be a rectangle but I'm just looking for a rough estimate. Thank you.

Answer 1

The square of the equilateral triangle is
St=a²/4*sqrt(3)=3.897114 km²
The square of the rectangle section is
Sr=b*c=50*25=1250 m².
So the number of section is ( where [] - means whole part of the number)
N=[ St/ Sr ] + 1= [ 3897114 / 1250 ] +1 =[3117.7]+1=3118 rectangle sections.